IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 23, NO. 2, APRIL 2000 137 Analysis of Process Models Armen Zakarian and Andrew Kusiak Abstract—Process modeling tools, such as the integrated Defi- nition (IDEF) methodology, allow for a systematic representation of processes in manufacturing, product development, and service applications. Most of the process modeling methodologies are based on informal notation, lack mathematical rigor, and are static and qualitative, thus difficult to be used for analysis. In this paper, a new analysis approach for process models based on signed directed graphs (SDG’s) and fuzzy sets is presented. A membership function of fuzzy sets quantifies and transforms incomplete and ambiguous information of process variables into an SDG qualitative model. The effectiveness of the approach is illustrated with an industrial example. The architecture of an intelligent system for qualitative/quantitative analysis of process models is presented. Index Terms—Approximate reasoning, fuzzy sets, process models, quantitative analysis. I. INTRODUCTION A PROCESS model includes a set of activities arranged in a specific order, with the clearly identified inputs and out- puts. The output may be either a product or service [1]. Each ac- tivity in a process takes an input and transforms it into an output with some value to a customer. Ideally, every transformation oc- curring in the process should add value to the input and create an output that is useful to a downstream recipient. An important advantage of process representation over tra- ditional functional approaches is in its structure. In this sec- tion, several of the existing process modeling methodologies and tools are described. They vary in scope, appearance, and theoretical foundations. A. CIM-OSA Computer integrated manufacturing—open systems archi- tecture (CIM-OSA) was developed by the ESPRIT Consortium AMICE [2]. The methodology facilitates system modeling through a process that includes system requirement definitions, system design specifications, and a system implementation description. Four system views (perspectives) are considered: functional, informational, resource, and organization [3]. B. OMM The object-oriented modeling methodology (OMM) for man- ufacturing includes analysis and design phases [4]. The first task of the analysis phase is to decompose the system’s functions into Manuscript received June 1, 1998; revised September 1, 1999. A. Zakarian is with the Department of Industrial and Manufacturing Sys- tems Engineering, University of Michigan-Dearborn, Dearborn, MI 48128-1491 USA. A. Kusiak is with the Intelligent Systems Laboratory, Department of Indus- trial Engineering, The University of Iowa, Iowa City, IA 52242-1527 USA. Publisher Item Identifier S 1521-334X(00)04971-5. Fig. 1. Petri net of an activity that uses two resources: (a) Petri net model, (b) initial marking, and (c) marking after has been fired. component functions using an approach similar to IDEF (dis- cussed later in this paper). After a functional model has been constructed, function tables, data tables, and operation tables are generated. In the design phase, the object-oriented paradigm is used to translate the function tables, data tables, and operation tables into an integrated information model. Classes consisting of an identifier, attributes, and methods are defined for compo- nents of the system. C. MOSYS MOSYS is a software tool for modeling the functional struc- ture, topology, and control rules of systems [5]. The functions of system are described with five building blocks: manufacture, transport, store, assemble, and test. These blocks are parametric and they can be customized to a specific application. D. Petri Nets A Petri net is a graphical modeling tool [6]. It consists of places (P), transitions (T), and arcs (see Fig. 1). Input arcs con- nect places with transitions, while output arcs start at a tran- sition and end at a place. Places may contain tokens. Transi- tions, which model activities, may occur (the transition fires), thus changing the state of the system (the marking of the Petri net). A marking in a Petri net is a vector that specifies the assignment of tokens to the places, i.e., / . An initial state of a Petri net is called the initial marking, . Transitions are only allowed to fire if they are enabled (all the preconditions for the activity are fulfilled). When the transition fires, it removes tokens from its input places and adds them to the output places. The number of tokens removed/added de- pends on the cardinality of each arc. Consider a process that con- sists of only one activity. To execute the activity, two resources have to be used. The net in Fig. 1(a) models this process, where 1521–334X/00$10.00 © 2000 IEEE